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chap0080 - Some Application Of Darcy-Weisbach Formula In...

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Some Application Of Darcy-Weisbach Formula In Steady Pipe Flows-II M.S. Ghidaoui (spring 2002) In this set of problems, both frictional losses and local (minor losses) are considered. In addition, both simple and branched pipe systems are analyzed in this chapter. In all the problems below, unless stated otherwise, assume water temperature is 15 ° C ( v = 1.13 x 10 -6 m 2 /S). Problem 1: A pipeline 20 km long delivers water from an impounding reservoir to a service reservoir the minimum difference in level between which is 100 m. The pipe of uncoated cast iron ( ε = 0.3 mm) is 400 mm in diameter. Local losses, including entry loss and velocity head amount to 10 V 2 /2g. 1. Calculate the minimum uncontrolled discharge to the service reservoir. 2. What additional head loss would need to be created by a valve to regulate the discharge to 160 l/s? Solution: H 1 2 1): The energy equation is: g V g V D fL g V Z P g V Z P 2 2 10 2 2 2 2 2 2 2 2 1 2 1 1 + + + + = + + γ γ Where, f (L/D)( v 2 /2g ) ~ Friction Losses 10 v 2 /2g ~ Minor (local) Losses P 1 = P 2 = 0; v 1 v 2 0
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g V g V D fL H Z Z 2 2 10 2 2 2 1 + = = - Or ε /D= 0.3/400 = 0.00075; Assume V= 2m/s Re= 7.27*10 5 From Moody chart: f=0.019 Using this f check whether or not the energy equation is satisfied: V min = (2g*100)/ (10+0.019*20,000/0.4) = 1.43 m/s The value assumed is 2 m/s but the value needed to satisfy the energy equation is 1.43 m/s. Not acceptable and we need to try again. Assume V=1.43 m/s New Re = 5.2*10 9 From Moody chart: f = 0.0192 Using f=0.0192 check whether or not the energy equation is satisfied: We obtain : V min =1.422 m/s The value assumed is 1.43 m/s and the value needed to satisfy the energy equation is 1.422 m/s. Close enough, we accept 1.422 m/s as our solution for velocity. The flowrate associated with this velocity is: Q min 179 l/s 2): Q = 160 l/s V = 1.273m/s Re = 4.5*10 9 f = 0.0193 ( 29 m h v g h h g V g V D fL v v 4 . 19 273 . 1 2 1 10 4 . 0 000 , 20 0193 . 0 100 2 10 2 100 2 2 2 = + × - = + + = where h v is additional valve losses Problem 2: A long, straight horizontal pipeline of diameter 350 mm and effective roughness size 0.03 mm is to be constructed to convey crude oil of density 860 kg/m3 and absolute viscosity 0.0064 Ns/m2 from the oilfield to a port at a steady rate of 7000
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